A cylindrical capacitor with inner conductor of radius $a$ and outer conductor of radius $b$ has outer conductor grounded and inner conductor charged to potential $V_{0}$ . At a cylindrical surface of radius $r (a < r < b)$ coaxial with the common axis of capacitor.

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Electric field is given by $\frac{V_{0}}{In (b / a) r}$ in magnitude

Electric field is given by $\frac{V_{0}}{2 In (b / a) r}$ in magnitude

Potential of sphere of radius a is given by $\frac{V_{0}}{In (b / a)}$

Potential of sphere of radius a is given by $\frac{V_{0} In (b / a)}{In (b / r)}$

answer is A.

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Detailed Solution

$V = V_{0^{-}} - \int_{a}^{r} E \cdot dr = \frac{V_{0} In (\frac{b}{r})}{In (\frac{b}{a})}, Where E = \frac{V_{0}}{rIn (\frac{b}{a})}$

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